EXISTENCE CONDITIONS OF PERMANENTAL AND MULTIVARIATE NEGATIVE BINOMIAL DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Eisenbaum, Nathalie; Maunoury, Franck
• 署名单位: Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1179
• 发表日期: 2017
• 页码: 4786-4820
• 关键词: inverse m-matrices; gamma-distributions; principal minors; determinants; inequalities; vectors; PROOF

摘要

Existence conditions of permanental distributions are deeply connected to existence conditions of multivariate negative binomial distributions. The aim of this paper is twofold. It answers several questions generated by recent works on this subject, but it also goes back to the roots of this field and fixes existing gaps in older papers concerning conditions of infinite divisibility for these distributions.